xy(x+y)-yz(y+z)-zx(z-x)
=y.[x.(x+y)-z.(y+z)]-zx.(z-x)
=y.(x2+xy-zy-z2)-zx.(z-x)
=y.[(x-z)(x+z)-y.(z-x)]-zx.(z-x)
=y.[-(z-x)(x+z)-y.(z-x)]-zx.(z-x)
=y.(z-x)(-x-z-y)-zx.(z-x)
=(z-x)(-xy-zy-y2-zx)
=(z-x)[-x.(y+z)-y.(y+z)]
=(z-x)(y+z)(-x-y)
=-(z-x)(y+z)(x+y)